Chapter 7 Data Structures for Computer Graphics (This chapter was written for programmers - option in lecture course) Any computer model of an Object must comprise three different types of entities: 1. Data - basic elements that consist of numerical values, characters, instructions, representation of attributes 2. Algorithm - data manipulation 3. Structure - data organization Structuring of data is a very important aspect of a database, which is a bank of the information to be processed and of the results, stored for future use. General databases The most popular data base models are relational, hierarchical, and network. 1. Relational database accesses data in a sequential form. (Figures 7.1, 7.2) Figure 7.2 Example of a relational database
2. Hierarchical database is a tree structure composed of a hierarchy of elements called nodes. (Figure 7.3) Hierarchical models are usually simple and fast, but only few relations in the real world are purely hierarchical. The other disadvantages of hierarchical structure are the hierarchical implementation usually creates redundancy and a danger of inconsistency (i.e. cannot implement non-manifold models) 3. Network database has a many-to-many relationship among its elements; elements at each level can be connected to many elements of the level above. (Figure 7.4) Basic data structure for graphics 1. Primitive data types - INTEGER, REAL, BOOLEAN (LOGICAL), CHARACTER 2. Static data structure (array) - fixed, predefined values and occupies fixed memory locations. 3. Dynamic data structure (pointer) - dynamic storage allocation
Static arrays (Homogeneous data structure) allow random access, is widely used in computer graphics. DIMENSION A (100) a = array[1..100] of real float a[100]; (FORTRAN) (PASCAL) (C) Static array operations: a. Traversal - accessing and processing each element of the array exactly once. (indexing operation) b. Insertion - adding a new element to an existing list. c. Deletion - removing an element from an existing list. Representation of polyhedral objects using static arrays (Figures 7.6, 7.7, 7.8) The three arrays used in the description of the cube are: 1. A vertex array listing the x, y, z coordinates of each vertex. 2. An edge array, pointing to the vertex array, indicating the two vertices at the end of each edge 3. A face array, pointing to the edge array, listing the edges that form each face Arrays: Face Edge Vertex
Structured data types record struct (PASCAL) (C) Figure 7.9 (a) PASCAL record implementation
Figure 7.9 (b) C struct implementation Pointers struct edge { struct point *pv1, *pv2; } e1.pv1 = &v1; e1.pv2 = &v2; Linked lists In C, a vertex array of variable size n can be dynamically allocated as vertex_header = (struct point*) calloc (n.sizeof(stuct point)); Single linked list has two fields: data and next link. Figure 7.10 Schematic diagram of a linked list
The original list would have to be expanded by the insertion of the new node through three operations: 1. Creation of the new node 2. Linking P2 to the new node 3. Linking the new node to the node P2 was originally point to Figure 7.11 Node insertion in a linked list These unused memory cells would also be linked to form a linked list of available nodes called AVAIL, which uses AVAIL as it list pointer variable. Figure 7.12 Use of an availability list for node insertion In C, the implementation could be struct node { int x, y; struct node *next_link; }; struct node *temp, *nlink; temp = (struct node*) malloc (sizeof(struct node)); temp->x = XNEW;
temp->y = YNEW; temp->next_link = NLINK; NLINK = temp; Double linked list has three fields: data, previous link, and next link. Figure 7.13 Double linked list Figure 7.14 Linked lists describing faces of representation of the structure a polyhedral object Figure 7.15 Schematic of Figure 7.14
Figure 7.16 A more general hierarchical linked data structure for polyhedral geometry Recursion E. g. Quadtree and octree data structures use of recursive methods in computer graphics applications.
Figure 7.17 Recursive subdivision of a two-dimensional region Trees Binary Tree - Each node of the tree has at most two children. Usually, binary tree is used in CSG (Constructive Solid Geometry) representation. The nodes in a binary tree are usually created by linked lists with pointers to its two children. Figure 7.18 A general tree structure Figure 7.19 Three structure for a quadtree
Geometry representations: 1. CSG (Constructive Solid Geometry) 2. B-Rep (Boundary Representation)